Question

Check if x+ 2 is a factor of 2x3
+ 4x 2
+x +2 help

Answer 1

(i) find the value of p

(ii) with the value of p, factorize the above expression completely.

factorization

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1 Answer

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answered Feb 25, 2019 by priya12 (-12,194 points)

Given expression is 2x3 – x2 – px - 2 and x – 2 is the factor.

(i) x – 2 = 0, x = 2 in expression

2(2)3 – (2)2 – p(2) – 2 = 0

16 – 4 – 2p – 2 = 0

10 – 2p = 0

p = 5

∴ 2x3 – x2 – 5x – 2 = (x – 2)(2x2 + 3x + 1)

The expression can be the written as

(2x2 + 3x + 1)(x – 2) or (2x + 1)(x + 1)(x – 2)

Answer 2

Answer:

Let the function be represented by f(x).

As x+2, exactly divides f(x),

−2 is a zero of f(x), hence f(−2)=0

f(x)=2x

3

+5x

2

−x−k

f(−2)=2(−2

3

)+5(−2

2

)+2−k=0

⇒0=−16+20+2−k

⇒k=6

Step-by-step explanation:

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